why are governmental marriage "licenses" required at all?
Obvious answer is because the government exists but God does not.
More seriously, religions used to be a more important part of government (and often ALL of government) and so they, of course, took on the job of managing a nations breeding stock. Religions, as part of their governing function, would record unions and offspring so that the community could have proper enforcement of their property rights (which wives you own and which children you own) and so that transgressions could be punished and also to keep track of the membership (and therefore the income potential and a projection of likely fighting strength).
An important part of herd (and political) management is deciding who should be allowed to breed with whom. You wouldn't want, for example, people of different classes or people of different races or religions marrying, but, while churches would register the marriages, the political decision to allow or disallow it wasn't always in their hands.
Although modern secular states still allow church services for those who wish to recognize their marriage that way, both registration of marriages and registration of offspring are done by the state. This has allowed the state to create policies about legal responsibilities of spouses to the state and to one another, legal responsibilities to children and also the responsibilities of the state to breeding pairs, and licensing restrictions have been relaxed over time. Marriages between people of different races and religions is now allowed.
Allowing same sex marriages is just one step further though, of course, responsibilities to offspring of the couple is complicated by the fact that any children produced will be the biological product of, at most, one of the partners - but many couples chose to be childless these days, use donated eggs or sperm, surrogacy or adoption so that bridge is already crossed.
There are still restrictions to marriage based on relatedness for e.g., I'm not aware of jurisdictions that permit sibling marriage, and while most places don't require a negative syphilis test to obtain a license as they did for the first half of the 1900s, some states are thinking about bringing blood tests back (to include HIV).
Still not allowed in any jurisdiction I know of - marriage to other species, inanimate objects or verbs (except figuratively). Marriage to deities is still practised by religious groups but are not recognized as marriages by the state.
Many jurisdictions also recognize "common law" marriage which is basically private agreement between two people that the government has realized it can't stop but needs to account for nonetheless to patch a hole in the legal framework.
